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Find the derivative using the quotient rule $\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$

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Basic Derivatives

· Quotient Rule in Differentiation

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{b\frac{d}{dx}\left(a\right)-a\frac{d}{dx}\left(b\right)}{b^2}$
· Power rule for derivatives

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$
· Sum Rule

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(a+b\right)=\frac{d}{dx}\left(a\right)+\frac{d}{dx}\left(b\right)$
· Derivative of a Constant

The derivative of the constant function ($[c]$) is equal to zero

$\frac{d}{dx}\left(c\right)=0$

Problem Analysis